scholarly journals $ L^2 $ -torsion of Hyperbolic Manifolds of Finite Volume

1999 ◽  
Vol 9 (3) ◽  
pp. 518-567 ◽  
Author(s):  
W. L�ck ◽  
T. Schick
Keyword(s):  
Finite Volume ◽  
Hyperbolic Manifolds

scholarly journals Analytic torsion of complete hyperbolic manifolds of finite volume

2012 ◽  
Vol 263 (9) ◽  
pp. 2615-2675 ◽  
Author(s):  
Werner Müller ◽  
Jonathan Pfaff
Keyword(s):  
Finite Volume ◽  
Hyperbolic Manifolds ◽  
Analytic Torsion

scholarly journals Integrality of volumes of representations

2021 ◽  
Author(s):  
Michelle Bucher ◽  
Marc Burger ◽  
Alessandra Iozzi
Keyword(s):  
Finite Volume ◽  
Hyperbolic Manifolds ◽  
3 Dimensional ◽  
Definition Of ◽  
Dehn Fillings

AbstractLet M be an oriented complete hyperbolic n-manifold of finite volume. Using the definition of volume of a representation previously given by the authors in [3] we show that the volume of a representation $$\rho :\pi _1(M)\rightarrow \mathrm {Isom}^+({{\mathbb {H}}}^n)$$ ρ : π 1 ( M ) → Isom + ( H n ) , properly normalized, takes integer values if n is even and $$\ge 4$$ ≥ 4 . If M is not compact and 3-dimensional, it is known that the volume is not locally constant. In this case we give explicit examples of representations with volume as arbitrary as the volume of hyperbolic manifolds obtained from M via Dehn fillings.

scholarly journals Collisions at infinity in hyperbolic manifolds

2013 ◽  
Vol 155 (3) ◽  
pp. 459-463 ◽  
Author(s):  
D. B. MCREYNOLDS ◽  
ALAN W. REID ◽  
MATTHEW STOVER
Keyword(s):  
Finite Volume ◽  
Hyperbolic Manifolds

AbstractFor a complete, finite volume real hyperbolic n-manifold M, we investigate the map between homology of the cusps of M and the homology of M. Our main result provides a proof of a result required in a recent paper of Frigerio, Lafont and Sisto.

Virtually spinning hyperbolic manifolds

2019 ◽  
Vol 63 (2) ◽  
pp. 305-313
Author(s):  
D. D. Long ◽  
A. W. Reid
Keyword(s):  
New York ◽  
Finite Volume ◽  
Hyperbolic Geometry ◽  
Spin Structure ◽  
Hyperbolic Manifolds ◽  
Geometric Topology ◽  
Academic Press ◽  
Finite Cover

AbstractWe give a new proof of a result of Sullivan [Hyperbolic geometry and homeomorphisms, in Geometric topology (ed. J. C. Cantrell), pp. 543–555 (Academic Press, New York, 1979)] establishing that all finite volume hyperbolic n-manifolds have a finite cover admitting a spin structure. In addition, in all dimensions greater than or equal to 5, we give the first examples of finite-volume hyperbolic n-manifolds that do not admit a spin structure.

scholarly journals Geodesic excursions into cusps in finite-volume hyperbolic manifolds.

1993 ◽  
Vol 40 (1) ◽  
pp. 77-93 ◽  
Author(s):  
María V. Melián ◽  
Domingo Pestana
Keyword(s):  
Finite Volume ◽  
Hyperbolic Manifolds

Finite volume and spectral methods applied to Pb-30%TI alloy solidification

2001 ◽  
Vol 11 (PR6) ◽  
pp. Pr6-151-Pr6-159 ◽  
Author(s):  
R. Guérin ◽  
M. El Ganaoui ◽  
P. Haldenwang ◽  
P. Bontoux
Keyword(s):  
Finite Volume ◽  
Spectral Methods ◽  
Ti Alloy ◽  
Alloy Solidification
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